Can I Automate Converting Groups of Triangles to Quads?
Select Similar

I think there cannot be an unique answer: there are multiple possible solutions to the problem of "grouping tris into quads". For example Blender is showing one of them, that cannot be said wrong in anyway. That's its automated way to solve the problem.

You'll have to write your own algorithm in order to specify what kind of index order should be followed while packing tris. Luckly, in the provided exmple you can take advantage of another tool: Select Similar.

As long as there is a recognizable pattern in the distribution of the triangles, as in your case, you can simply select all the vertices that are ruining your quads and dissolve them.

Pick one vertex in the middle of the "future" quad, run Select Similar command with "amount of connecting edges" option, then press X and choose Dissolve vertices